Strongly interacting Fermi systems in 1/N expansion: From cold atoms to color superconductivity

TL;DR

This paper explores the 1/N expansion method to include quantum fluctuations in nonrelativistic and relativistic Fermi systems, analyzing critical temperatures and phase diagrams relevant to cold atoms and dense quark matter.

Contribution

It extends the 1/N expansion approach to calculate next-to-leading order corrections across the BCS-BEC crossover and applies it to relativistic systems like color superconductivity.

Findings

Extrapolation from mean-field is valid mainly on the BCS side.

Corrections to critical temperature are proportional to the mean-field ratio T_c/μ.

Fluctuation effects are significant even deep in the BCS regime.

Abstract

We investigate the 1/N expansion proposed recently as a strategy to include quantum fluctuation effects in the nonrelativistic, attractive Fermi gas at and near unitarity. We extend the previous results by calculating the next-to-leading order corrections to the critical temperature along the whole BCS-BEC crossover. We demonstrate explicitly that the extrapolation from the mean-field approximation, based on the $1/N$ expansion, provides a useful approximation scheme only on the BCS side of the crossover. We then apply the technique to the study of strongly interacting relativistic many-fermion systems. Having in mind the application to color superconductivity in cold dense quark matter, we develop, within a simple model, a formalism suitable to compare the effects of order parameter fluctuations in phases with different pairing patterns. Our main conclusion is that the relative correction to the critical temperature is to a good accuracy proportional to the mean-field ratio of the critical temperature and the chemical potential. As a consequence, it is significant even rather deep in the BCS regime, where phenomenologically interesting values of the quark-quark coupling are expected. Possible impact on the phase diagram of color-superconducting quark matter is discussed.